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How many future measures can there be?

Published online by Cambridge University Press:  09 January 2002

KATALIN MARTON  and
PAUL C. SHIELDS
KATALIN MARTON
Affiliation:
Mathematics Institute, Hungarian Academy of Sciences
PAUL C. SHIELDS
Affiliation:
Mathematics Department, University of Toledo, Toledo, OH 43606, USA (e-mail: [email protected])
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Abstract

The question addressed in this paper is the worst-case growth rate, for ergodic processes, in the number of conditional measures on n-steps in the future, given the past, that are a fixed distance apart. It is shown that if error is measured using the variational (i.e. distributional) distance then doubly exponential growth is possible, while if error is measured using the \bar{d}-metric then more than exponential growth is possible. The question of whether doubly exponential growth is possible in the \bar{d}case is left open.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 22 , Issue 1 , February 2002 , pp. 257 - 280
Copyright
2002 Cambridge University Press

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